Question

Explain how to solve an equation of the form x p/q = a for nonzero integer x,p,q, and a. what is x in terms of a,p, and q?

Answer 1

Answer:

The value of x from the given equation in terms of a,p and q is $\frac{aq}{p}$

Therefore  $x=\frac{aq}{p}$

Step-by-step explanation:

Given equation is $\frac{xp}{q}=a$ for nonzero integers x,p,q, and a.

To find the value of x in terms of a,p and q :

$\frac{xp}{q}=a$

Multiplying by $\frac{q}{p}$ on both sides we get

$\frac{xp}{q}\times \frac{q}{p}=a\times \frac{q}{p}$

$\frac{xpq}{qp}=\frac{aq}{p}$

$x=\frac{aq}{p}$

Therefore the value of x in terms of a,p and q is  $\frac{aq}{p}$

Therefore  $x=\frac{aq}{p}$

Answer 2

Answer: x in terms of a, p, q is $x=\frac{aq}{p}$

From the given equation we see that p/q is multiplied to x. Or we can also say that p is multiplied to x and q is divided.

So to get x alone, we will multiply both sides by q and divide by p.

So the solution is:

$x\cdot\frac{p}{q}=a\\x\cdot\frac{p}{q}\cdot\frac{q}{p}=a\cdot\frac{q}{p}\\x=a\cdot\frac{q}{p}\\x=\frac{aq}{p}$

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